CONDITIONAL SOJOURN TIMES OF PROCESSOR-SHARING QUEUES

Queues operated by a processor-sharing mode have important applications in many modern systems. However, because of the simultaneous sharing of service capacity by all customers, the distribution function and moments of the sojourn time are difficult to derive, even with a given initial condition. In addition, when a limit on the number of customers in the system is enforced to ensure the quality of service, the sojourn time becomes more complicated. In recent literature, the distribution function is obtained via the Laplace-Stieltjes transform. In this paper, we take a pure algebraic approach to derive the moments of the sojourn time. We obtain an iterative formula and use it to investigate properties of the conditional sojourn time. The approach is simple and intuitive, and applies to queues with multiple class customers as well.